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# Phase-locked Loops - Theory and Design

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The invited talk at ITRI in 2011.

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### Phase-locked Loops - Theory and Design

1. 1. Phase Locked Loops Theory and Design Chien-Jung Li Department of Electronic Engineering National Taipei University of Technology
2. 2. Outline • Frequency Synthesis Techniques • Frequency Synthesizers based on the Phase-Locked-Loop (PLL) • Loop Analysis and Stability • Components in a PLL • Noise Analysis • PLL Architectures • Simulation Examples Department of Electronic Engineering, NTUT2/140
3. 3. Generic Transceiver Front End Bandpass Filter LNA Duplexer Antenna v Frequency Synthesizer LO PA • Local oscillator (LO) provides the carrier signal for both the receive and transmit paths. • If the LO output contains phase noise, both downconverted and upconverted signals are corrupted. Department of Electronic Engineering, NTUT3/140
4. 4. Effect of Phase Noise in Receivers f 0f Wanted Signal LO Output Wanted Signal Downconverted Signal f Downconverted Signals ff 0f Wanted Signal LO Output Interferer • Reciprocal Mixing Department of Electronic Engineering, NTUT4/140
5. 5. Effect of Phase Noise in Transmitters f 1f Wanted Signal Nearby Transmitter 2f f 0f Multi-carrier signal (or OFDM) f 0f • Receiver Desensitization • Orthogonality Department of Electronic Engineering, NTUT5/140
6. 6. Frequency Synthesis  v t t • Meaning of frequency synthesis Generation of a frequency or frequencies that are exact multiples of a reference frequency. Usually the reference is very precise and the synthesized frequencies are selectable over some range of whole-number multiples of a submultiple of the frequency at out ref n f f M  where n and M are integers, n varies from Nmin to Nmax, and M is constant. 1T 1 1 f  V f f 1f • Meaning of frequency reff Department of Electronic Engineering, NTUT6/140
7. 7. Transformation to and from Voltage or Current A B1f Frequency Discriminator  C D d dt Voltage Controlled Oscillator (VCO) Phase Detector Phase Modulator 1 1v Af 2 1f Bv   1 1f dt 2 1v C  2 2Dv 3 2 d f dt V/Hz Hz/V V/rad or V/cycle rad/V or cycle/V Department of Electronic Engineering, NTUT7/140
8. 8. Demonstration of the Transfer Functions              rms rms rms rms rms 1 rad 2 V rad rad 1 1 V 2 V 2 V V 0.32 V V cycle cycle 2 rad AV Phase Modulator 1 rad/V Phase Detector 2 V/Cycle 220 MHz VCO 1.5 MHz/V 1 k 200 MHz ICO 1 MHz/mA 100 MHz signal Low-pass Filter 50 MHz Cut-off Frequency Discriminator 5 V/MHz A B D • RMS voltage at point A: Modulation voltage (1 Vrms at 10 kHz)    1 rms MHz 0.32 V 1.5 0.48 MHz V f      rms 2 0.32 V MHz 1 0.32 MHz 1 k mA f     rms 5 V 0.48 MHz-0.32 MHz 0.8 V MHz DV C Department of Electronic Engineering, NTUT8/140
9. 9. Mathematical Operations on Frequency (I) • Addition and Subtraction: The Mixer RF LO IF    cos 2RF RF RFv t A f t            cos 2 cos 2IF RF LO RF RF LO LOv t v t v t A f t B f t         For the practical mixer with nonlinear operation: IF RF LOf mf nf  Department of Electronic Engineering, NTUT9/140    cos 2LO LO LOv t B f t           cos 2 cos 2 2 RF LO RF LO RF LO RF LO AB f f t f f t                         cos2 cos2 for 0 2 RF LO RF LO RF LO AB f f t f f t            , cosIF m nv t K m n   2 RF RFf t    2 LO LOf t   where and or we can say the intermediate frequency is:
10. 10. Mathematical Operations on Frequency (II) • Frequency Dividers  Subharmonically synchronized oscillators  Digital dividers • Frequency Multiplier  Full-wave rectifier (frequency doubler)  Harmonically tuned class-C amplifier  Step-recovery diode (SRD) 1 powerG N  10/140 Department of Electronic Engineering, NTUT
11. 11. Frequency Synthesis Techniques • Direct Analog Synthesis (DAS) • Direct Digital Synthesis (DDS) • Indirect Synthesis - Phase-Locked Loops (PLLs) • Hybrid DDS/PLL Department of Electronic Engineering, NTUT11/140
12. 12. Direct Analog Synthesis (DAS) I • Frequency generated by mixed frequencies 1f 2f 3f 2Nf 1Nf Nf outf filter1 filter2 filter3 filterN-2 filterN-1 filterN out a bf mf nf  Department of Electronic Engineering, NTUT12/140
13. 13. Direct Analog Synthesis (DAS) II • More stages are required for flexibly frequency planning. 1f 2f 3f 2Nf 1Nf Nf filter1 filter2 filter3 filterN-2 filterN-1 filterN filter1 filter2 filter3 filterN-2 filterN-1 filterN outf 1f 2f 3f   2Nf   1Nf Nf Department of Electronic Engineering, NTUT13/140
14. 14. Direct Digital Synthesis (DDS) I • Waveform construction is based on the lookup table (LUT) and a digital to analog converter (DAC) • Direct synthesis • Generated frequency is lower than input frequency ref cf f Department of Electronic Engineering, NTUT14/140
15. 15. Direct Digital Synthesis (DDS) II • Hardware technique to reduce the spur level of a DDS • Reduce bandwidth 1000MHz 100-150MHz 1100-1150MHz 110-115MHz div-by-10 DDS Filter Frequency Divider 0f outf BW=50MHz BW=15MHz reff Department of Electronic Engineering, NTUT15/140
16. 16. Hybrid DDS/DAS • Scheme to increase a DDS output bandwidth 1f 2f 3f   2Nf   1Nf Nf outf filter1 filter2 filter3 filterN-2 filterN-1 filterN DDS Frequency Divider reff Department of Electronic Engineering, NTUT16/140
17. 17. Indirect Frequency Synthesis (PLL) II PFD LPF Frequency Divider reff outf /N • The main goal of the PLL is to sync the divided oscillator frequency with the reference frequency outf N reff  out reff N f out reff N f  VCO Department of Electronic Engineering, NTUT17/140
18. 18. Fractional-N Frequency Synthesis • Lower division ratio N to reduce inband phase-noise gain • Effectively produce a fractional division value • Generally employee a delta-sigma modulator for division ratio dithering PFD LPF Dual-modulus Frequency Divider reff outf /N, (N+1) FCW Department of Electronic Engineering, NTUT18/140
19. 19. Principle of PLL Operation vco con out reff f Department of Electronic Engineering, NTUT19/140 • The main goal of the PLL is to sync the divided oscillator signal with the reference signal (usually a pure sinusoid).
20. 20. Phase-Locked Loop Analysis
21. 21. The Phase-Locked Loop • PFD: Phase Frequency Detector • LPF: Loop Filter • VCO: Voltage Controlled Oscillator PFD LPF Frequency Divider reff outf /N VCO • /N: Divied-by-N Frequency Divider Department of Electronic Engineering, NTUT21/140
22. 22. Feedback System  iV s  oV s  G s  H s error          o i oV s V s V s H s G s             i oG s V s V s G s H s           1 o i V s G s V s G s H s   Department of Electronic Engineering, NTUT22/140 Closed-loop transfer function G(s)H(s) is the open-loop transfer function
23. 23. Loop Analysis – Use Frequency as I/O Frequency Divider  reff s  outf s 1 s pK  F s vK 1 N Phase differenceFrequency difference  outf s N • Relation between Input and Output Frequencies    p v K G s F s K s    1 H s N                11 1 p v out pref v K F s Kf s G s s Kf s G s H s F s K N s     Department of Electronic Engineering, NTUT23/140
24. 24. Loop Analysis – Use Phase as I/O Frequency Divider  ref s  out s pK  F s vK s 1 N • Relation between Input and Output Phases Phase difference Frequency to Phase     v p K G s K F s s    1 H s N                11 1 v p out vref p K K F ss G s s Ks G s H s K F s N s       Department of Electronic Engineering, NTUT24/140
25. 25. Loop Transfer Functions                 0 0 0 01 1 p po i p p K F s K s K F s K G s T s K F s K Ns Ns K F s K G s H s           T(s) : closed-loop PLL transfer function  G(s) : forward-path transfer function  F(s) : loop filter transfer function  Kp: phase detector gain  K0/s: VCO transfer function    1 0G s H s  • A PLL is unstable when     1 0 dB@ 180G s H s       The condition of unity open loop gain and a phase angle of 180 degrees must be avoided.  H(s) : feedback-path transfer function  G(s)H(s) : open-loop transfer function or Department of Electronic Engineering, NTUT25/140
26. 26. PLL Response without a Loop Filter (I)   0 0 0 01 F p LPFo Fi p LPF K K K K s NT s N N KK K K Ns ss N           • 3 dB cutoff frequency is KF/N = KpKLPFKo/N   LPFF s K • Without the loop filter, the feedback loop is equivalent to a DC gain of N plus a low-pass filter with cutoff at .0 log dB 0 FK N    20logN 3 dB 0 Department of Electronic Engineering, NTUT26/140
27. 27. PLL Response without a Loop Filter (II) • The open loop gain has a slope of -6dB/octave or -20dB/decade for all frequencies. • The phase angle is always -90 degrees at all frequencies. Hence with no low-pass filter, the PLL is always stable. But the main drawback is that designers loose control over the loop. • The simplest PLL is called a type-I loop because the open-loop gain has one pole at DC (pure integration). It is also a first-order loop because the open-loop gain has one significant pole.      p vK F s K G s H s Ns  Department of Electronic Engineering, NTUT27/140
28. 28. Single Pole Loop Filter • The function of the LPF is to filter out any high frequency harmonics in the loop that might cause the loop to go out of lock, and also to stabilize the loop. • Adding a LPF also affects the loop response including parameters such as the loop time response, bandwidth, and the damping factor.    1 LPF p K F s s    • If we add a low-pass filter with a pole located at , the loop will be still type-I, but it will become a second-order loop.     1 1 p LPF v F p p K K K K N NG s H s s s s s                     p Department of Electronic Engineering, NTUT28/140
29. 29. Bode Plot of Forward-path Transfer Function minL log m  mG  6 dB/oct 1020log FK 10 max20log N 10 min20log N maxL p1m  90  135  180   mG  12 dB/oct • Where the curves cross, the open-loop gain equals unity.       1 G s G s H s N    G s N (forward-loop gain ) Department of Electronic Engineering, NTUT29/140
30. 30. Bode Plot of Open-loop Transfer Function log m    m mG H  6 dB/oct 1020log FK N 0 dB L p1m  90  135  180   mG  12 dB/oct • Where the curves cross, the open-loop gain equals unity.       1 G s G s H s N    G s N (forward-loop gain ) Phase margin Department of Electronic Engineering, NTUT30/140
31. 31. Natural Frequency and Damping ratio             0 0 1 1 1 1 1 1 F ppo F Fi p F p p K ss K F s K sG s NK T s KG s H s K F s K Ns sNs K sNs                            0 F p n p K N      0 1 1 1 2 2 2 p p p n F N K          is geometric mean of the loop bandwidth in the absence of a filter and the filter corner frequency. 2 2 2 2 2 2 2 2 p F p F n p F n n n n p K K N K s s s s s s N                   Characteristics equation • Prototype second-order equation •Natural frequency •Damping ratio Department of Electronic Engineering, NTUT31/140
32. 32. Closed-Loop Gain for Large Damping Ratio As long as damping ratio is greater than one, the poles are real and a tangential plot of closed loop gain looks 20logN 6 dB/oct 12 dB/oct log m  out ref f s f 2 2 0 2 1 1 1         2 1 1 1 2 p        The characteristics are similar to the case with no loop filter, except for the increasing rate of attenuation in fout/fref beyond approximately the filter corner frequency . 2 1p n ns      • The poles of the closed-loop function are located at 0 p Department of Electronic Engineering, NTUT32/140 p
33. 33. Close-loop Responses 0 F p n p K N      0 1 1 1 2 2 2 p p p n F N K          • As decreases toward , the damping ratio decreases and the phase shift at increases. Correspondingly, the transient response of the loop becomes less damped (more ringing) and the response peaks near . p 0 0 n m n  0m  • For large damping, the response is similar to that for no filter but, as the damping ratio decreases, the response peaks and the peak moves to a lower frequency relative to .0 Department of Electronic Engineering, NTUT33/140
34. 34. Relative Stability – Phase Margin • Left figure shows the phase margin (relative stability) as a function of the damping factor. More highly damped loops are safer, in that more parameter variation is allowable before instability occurs. log m    m mG H  6 dB/oct 1020log FK N 0 dB L p1m  90  135  180   mG  12 dB/oct Phase margin • With a single-pole low-pass filter, the loop is inherently stable, sine -180o phase shift cannot be attained for any finite frequency. (not always true practically) Department of Electronic Engineering, NTUT34/140
35. 35. Transient Response reff outf  G s 1 N e 1N 2N 1 refN f 2 refN f  2 1N N e 1 2 1 ref N f N       t 0t  t oldf newf Synthesizer output frequency A B C D Overshot Ringing • Lower damping ratio brings a higher percent overshoot can cause the loop to go out of lock. (more unstable) • Narrower bandwidth with smaller damping ratio and longer settling time. Department of Electronic Engineering, NTUT35/140
36. 36. Settling Time • Settling Time The frequency error changes one decade approximately each 2.3 time constant, that is,    0 02.3 log f T f T    oldf newf  0f 0t  t T  f T • Example (no filter) 3 -1 1 MHz/cycle 10 secFK   10 kHzreff  11 MHz 10 MHzoutf   Find the settling time for the output frequency of 10.1 MHz is attained. 6 0 10 1000 1000 FK N     0 2.3 1 log 2.3 ms 0.1 T   Department of Electronic Engineering, NTUT36/140
37. 37. A Pole-Zero Filter • A pole-zero filter is a low pass filter with a pole frequency and a zero frequency . The addition of a pole in the transfer function causes the transfer function slope to drop at a rate of 6 dB per octave whereas the addition of a zero in the PLL transfer function has the opposite effect. The pole-zero filter transfer response is given by            1 1 z p s F s s • The open loop transfer function is:           1 1 p v zp v p K K sK F s K G s H s Ns Ns s          p z 6 dB/oct 12 dB/oct log m zp 6 dB/oct • The closed-loop transfer function is:       0 01 po i p K F s K s T s K F s K Ns      Department of Electronic Engineering, NTUT37/140
38. 38. Open-Loop Gain with a Pole-Zero LPF • In this case, the location of the pole is always before the zero frequency. Given the pole frequency location, a zero can be placed after the so as to avoid the magnitude from crossing the unity gain axis at a slope of 12 dB per octave, and therefore avoiding instability. To determine the closed loop response, simply plot T(s),     2 1 1 p F z p F p F p z K s NT s N K K s s N N                 0 F n p p K N      1 2 p n n z             6 dB/oct 12 dB/oct log m zp 6 dB/oct  2 2 2 1 2 z n n n s N s s         Department of Electronic Engineering, NTUT38/140
39. 39. Open-Loop Gain with a Pole-Zero LPF • From the results, selecting the pole frequency sets the natural frequency (and subsequently the loop bandwidth) and selecting the zero (based on the pole location in the open loop gain response) determines the desired percentage overshoot. Therefore, a pole-zero filter allows the designer to select the loop bandwidth and the damping factor independently and still achieve stability. 0 F n p p K N      1 2 p n n z             Department of Electronic Engineering, NTUT39/140
40. 40. Components in PLLs
41. 41. Phase Detector (PD) – Mixer  1 2cosd dv A    2i i if     1 2coss sv A    • The balanced mixer IF d sv v v     1 2 1 1 2cos cos 4IF d sv A A f t         1 2f fFor filtered-out by the LPF  1 2  2  1 2 2        IF dv A     and is very small 1 1 12 f    2 2 22 f    IFv Phase of signal 1 Phase of signal 2 Department of Electronic Engineering, NTUT41/140
42. 42. A B C 0 0 0 0 1 1 1 0 1 1 1 0 Phase Detector (PD) – EXOR A B C 1 0 1 0 T  A B ppV C A B  average value of v(C) ppV 1.0 0.5 0 0.5 1.0 T • The exclusive-OR 1 0 1 0 T A B ppV C A B  Department of Electronic Engineering, NTUT42/140
43. 43. Phase Detector (PD) – SR-FF S R QA B C T Av Bv ppV  Cv 0 1 2 average value of v(C) T ppV A B C 0 0 N 0 1 0 1 0 1 1 1 X • S-R Flip-Flops Department of Electronic Engineering, NTUT43/140
44. 44. Phase/Frequency Detector (PFD) A lagging B ( same ) • Detectable range : -2π~ 2π CLK D Q CLR Q D CLR CLK A B 1 QA QB A B QA QB A BQ Q 2 4 24   A leading B ( same ) A B QA QB  Department of Electronic Engineering, NTUT44/140
45. 45. Two General Types of PFD T t ref(t) div(t) ref/2(t) div/2(t) e(t) 1 -1 • XOR-Based PFD ref(t) div(t) up(t) dn(t) e(t) 1 0 -1 T t • Tri-state PFD Department of Electronic Engineering, NTUT45/140
46. 46. Typical Dead-Zone for Various PFDs Type Dead Zone Conventional ~800ps NC-PFD ~160ps TSPC-PFD ~210ps MPTPFD ~10ps • Commercial product Motorola MC4044 using conventional PFD introduce 30 degree dead-zone@20MHz (~400ps). • The first XOR-based dead-zone free design was proposed by Analog Device (AD9901). 1f 2f UP UP DN DN Department of Electronic Engineering, NTUT46/140
47. 47. Dead-zone Problem of PFDs • In a PLL, the contribution of every block is essential to the total phase noise if a high-quality frequency synthesizer is the goal. • If the input frequency reference to be compared is as high as several MHz, the linearity of the phase detector becomes essential. • In the passband of the PLL, the output phase noise depends on noise contribution from the phase detector, loop filter and frequency divider. • In charge pump based PLL, there are more problems. Department of Electronic Engineering, NTUT47/140
48. 48. The Principle of PFD and Dead-Zone Problem • The PFD operates as a frequency detector initially and as phase detector finally to achieve loop lock. • The dead-zone problem: － When two signals have the same frequency and almost identical phase, the PFD block is not able to generate a proper output signal so that an identical phase may be obtain. － This uncertainty leads to phase noise (jitter in time domain) and generation of spurious at the output of VCO. AND gate switch threshold ref(t) div(t) up(t) dn(t) 1 0 1 0 ref(t) div(t) up(t) 1 0 1 0 dn(t) ref(t) div(t) 1 0 1 0 up(t) dn(t)   Department of Electronic Engineering, NTUT48/140
49. 49. Solve the Dead-Zone Problem • Delayed reset path • Inphase operation • Need accurate timing analysis • Low spurious tones • Bad linearity • Alternatively current output • Non-inphase operation • More power consumption at lock state • Current mismatch with CP is the issue • High spurious tones • Good linearity • XOR-Based PFD • Tri-state PFD Department of Electronic Engineering, NTUT49/140
50. 50. Improvement of PFD Linearity 22 2 0  0 22 0 Department of Electronic Engineering, NTUT50/140
51. 51. Charge-Pump Phase Detector • The most popular phase-detector type is both a charge-pump (CP) detector and a phase-frequency detector (PFD), the terms, the charge-pump PD and PFD, are sometimes interchangeably. • The PFD acts as a phase detector during lock and provides a frequency-sensitive signal to aid acquisition when the loop is out of lock. • The charge pump is so named because it is supposed to deliver a charge proportional to phase error to the loop filter. PFD Charge Pump Switched Output (analog) Charge Up Charge Down CU (digital) CD (digital) RD VD Department of Electronic Engineering, NTUT51/140
52. 52. Charge Pump PFD PFD AQ BQ pC DDV A leading B ( same ) RD VD QA QB  VCP VCP t Department of Electronic Engineering, NTUT52/140 RD VD
53. 53. Charging Current RD VD CU CD Current Out Department of Electronic Engineering, NTUT53/140
54. 54. Charge Pump (Current Source and Sink) PFD AQ BQ DDV RD VD LZ oV DDV R 1M 2M 1 1 W L 2 2 W L 2D oI I1DI GSV oV sink current   21 1 2 DD GS D GS thn V V I V V R        22 2 2 D GS thnI V V    2 2 2 2 2 1 1 1 1 1 D D I W L W I W L W      DDV R 1M 2M1 1 W L 2 2 W L 2D oI I 1DI SGV oV source current   2 1 1 2 DD SG D SG thp V V I V V R        2 2 2 2 D SG thpI V V    2 2 2 2 2 1 1 1 1 1 D D I W L W I W L W      • Saturation region: DS GS thnV V V  GS thnV V • Saturation region: SD SG thpV V V  SG thpV V Department of Electronic Engineering, NTUT54/140
55. 55. Early Effect DDV R 1M 2M 1 1 W L 2 2 W L 2D oI I1DI GSV oV sink current    22 2 ,1 2 D GS thn DS DS satI V V V V        1 L   • Channel length modulation and Early effect DI DS oV V (prefer a long channel length) 2 1 1A o D o D V r I I I     (prefer a high output resistance) Department of Electronic Engineering, NTUT55/140
56. 56. Cascode Connection and Switch  3 3 2 21o o m o oR r g r r   DI DS oV V • Cascode connection increases output resistance PFD AQ BQ DDV RD VD LZ oV DDV R 1M 2M 1 1 W L 2 2 W L 2D oI I1DI GSV oV sink current BQ switch 3M 2 thnV V  • Need excess gate-source voltage V BQ is a digital signal (0~VDD) thnV Cascoded (with switch) Department of Electronic Engineering, NTUT56/140
57. 57. Current Mismatch DI DS oV V Department of Electronic Engineering, NTUT57/140
58. 58. Spurs and CP Non-ideal Effect tsource toff tsink Isink Isource tcomp • Reference Spurs - current leakage - current source mismatch (a) current mismatch with different output node voltage (b) unequal switching time • Non-reference Spurs - crosstalk (a) dual loop (b) interferences - non-crosstalk (a) fractional spurs (b) interferences (c) dual loop references mixing (d) prescaler miss counting Department of Electronic Engineering, NTUT58/140
59. 59. Charge-Pump Switching Time • When the charge-pump(CP) based PLL is used, the CP is also the bottle neck since the PFD can’t distinguish input edges separated by less than the CP switching time. CPI CPI PFD PFD CP CP Department of Electronic Engineering, NTUT59/140
60. 60. Dead-Zone Elimination and Spurs • In conventional PFD, the problem of the CP current sources mismatch is amplified by the number of additional delays in the reset path. ref(t) div(t) 1 0 1 0 up(t) dn(t)   ref(t) div(t) 1 0 1 0 up(t) dn(t)   periodic output! +ICP -ICP Department of Electronic Engineering, NTUT60/140
61. 61. Dead-Zone Issues • In charge pump based PLL, the dead-zone problem is not only considered in PFD design but charge pump. • As reference frequency goes higher, the dead-zone issue is more serious, because the linearity highly depends on the dead-zone. • In charge pump design, it’s hard to achieve low power consumption, fast current switching and perfect current mismatch. Department of Electronic Engineering, NTUT61/140
62. 62. Frequency Divider PFD LPFreff outf /N VCO divf inf  / 1M M  Prescaler P S inf divf Program counter Swallow counter Reset Modulus control Channel selection •Pulse Swallow Frequency Divider 1 in in T f  1 inM T  1 inS M T   inP S MT      1div in in inT S M T P S MT S PM T      (1) Start with divided-by-(M+1) Total counts of program counter = P cycles (2) Change to divided-by-M 1 div div T f    1 1 div in inf f f S PM N    2, 8, 4 4 8 2 20M P S N        Department of Electronic Engineering, NTUT62/140
63. 63. Asynchronous Divider J Q K C J Q K C J Q K C 1 1 1 1 1 1 inf 2 inf 4 inf 8 inf inf 2inf 4inf 8inf outf inf 2inf 4inf 8inf outf Department of Electronic Engineering, NTUT63/140
64. 64. Synchronous Divider (2 versions) J Q K C J Q K C J Q K C J Q K C J Q K C 1 1 2inf 4inf 8inf 16inf 16inf Department of Electronic Engineering, NTUT64/140
65. 65. Spikes in Synchronous Divider 2inf 4inf 8inf outf 2inf 4inf 8inf outf 2inf late 8inf early • Racing in synchronous divider producing output spikes Department of Electronic Engineering, NTUT65/140
66. 66. Synchronous Divider w/ Enable J Q K C J Q K C J Q K C J Q K C J Q K C J Q K C 1 1 J Q K C J Q K C J Q K C J Q K C J Q K C J Q K C 1 1 •Parallel Enable •Serial Enable Department of Electronic Engineering, NTUT66/140
67. 67. Direct Variable Frequency Divider Department of Electronic Engineering, NTUT67/140
68. 68. Type and Order of the Loop Frequency Divider  ref s  out s pK  F s vK s 1 N            1 G s N s T s G s H s D s    • The simplest PLL is the type-I loop because the open-loop gain has one pole at DC (pure integration). It is also a first-order loop because the open-loop gain has one significant pole.   1 1 0 n n n nN s a s a s a       1 1 0 m m m mD s b s b s b     Order = m (m roots) Type = n (n roots at DC) Department of Electronic Engineering, NTUT68/140
69. 69. Filter First-order Type 1 • First order, type I (no filter) 1R iv ov 2R L log m0 dB G 6 / .dB oct 2 1 2 o LPF i v R G v R R    A 3R iv 4R ov  A 4 3 o LPF i v R G v R      Department of Electronic Engineering, NTUT69/140
70. 70. Filter Second-order Type I • Second order, type I (Lag-and-lead filter) 1R iv ov 2R 1C A 3R iv 5R ov 2C 4R L log m0 dB G 12 / .dB oct 6 / .dB oct zp      1 1 z LPF p s G s   2 1 1 z R C 1 2 1 1 p R R C    1 1 z LPF p s G s         4 5 2 4 5 1 z R R C R R      5 2 1 p R C Department of Electronic Engineering, NTUT70/140
71. 71. Filter Second-order Type 1 • Second order, type I (Lag filter) 1R iv ov 2R 1C L log m0 dB G 6 / .dB oct p 12 / .dB oct A 3R iv 4R ov 2C  A      2 1 2 1 1 LPF p R G sR R       4 3 1 1 LPF p R G sR        1 1 2 1 1 1 p C R R   4 2 1 p R C Department of Electronic Engineering, NTUT71/140
72. 72. Filter Second-order Type II • Second order, type II (Integrator and lead filter) L log m0 dB G 12 / .dB oct 6 / .dB oct z A 1R iv 2R ov C  A      1 1 1 1 z LPF s G R C s   2 1 z R C Department of Electronic Engineering, NTUT72/140
73. 73. Filter Third-order Type II • Third order, type II (Integrator plus lead-lag filter) L log m0 dB G 12 / .dB oct p 12 / .dB oct 6 / .dB oct z A 1R iv 2R ov 2C 1C  A A 3R iV 4R oV 3C 5R 4C A 1 1 1 1 1 z LPF p s G R C s s                           3 3 1 1 1 z LPF p s G R C s s     2 1 2 1 z R C C   2 2 1 p R C   4 3 1 z R C   5 4 1 p R C Department of Electronic Engineering, NTUT73/140
74. 74. Filter Third-order Type II • Third order, type I (imperfect integrator plus lead-lag filter) L log m0 dB G 6 / .dB oct  2p 12 / .dB oct 6 / .dB oct z 1p 12 / .dB oct A 1oA R A  A Department of Electronic Engineering, NTUT74/140
75. 75. Oscillator • Oscillator provides a sinusoidal signal  v t t 1 1 f  V f f 1f  v t t 1 1 f  V f f 1f Department of Electronic Engineering, NTUT75/140
76. 76. Voltage Controlled Oscillator (VCO) • VCO is an oscillator of which frequency is controlled by a tuning voltage • VCO is a simple FM modulator vcof tuneV tuneV Department of Electronic Engineering, NTUT76/140
77. 77. VCO Sensitivity and Tuning Linearity • Frequency Range • Frequency tuning characteristics - Sensitivity (Hz/Volt) - Linearity VK f V   vcof tunev ,0tv 0f maxf minf ,mintv ,maxtv v f Ideal (perfect) Piecewise good Piecewise good Poor Department of Electronic Engineering, NTUT77/140
78. 78. Important Figures • Output Power (@50 Ohm) • Frequency Stability: frequency drifting • Pushing and Pulling Figures • Harmonics • Phase Noise (Jitter) Department of Electronic Engineering, NTUT78/140
79. 79. Phase Noise and Jitter      1 Hz 10log 10log dBc Hz 2 noise carrier S fP L f P      • Phase Noise • Jitter  Cycle jitter cn nT T T     2 1 1 lim N c cn n n T N       Cycle-to-cycle jitter 1ccn n nT T T     2 1 1 lim N c ccn n n T N       Absolute jitter (long-term jitter, accumulated jitter) of N cycles       1 1 N N abs n cn n n T N T T T           2 1 1 lim N c ccn n n T N      for white noise sources   0 2 abs cc f T t t    and 2cc c  Department of Electronic Engineering, NTUT79/140
80. 80. Relation of Phase Noise and Jitter • Relationship between the SSB phase noise and the rms cycle jitter: (Weigandt et al.)     3 2 0 2 cf L f f     • Relationship between the SSB phase noise and the rms cycle jitter: (Herzel and Razavi)         3 2 0 22 3 4 0 4 8 cc cc L             • Self-referred jitter and phase noise with white noise: (Demir et al.)     2 0 2 2 4 2 0 f c L f f f c      2 t t c     20 2 cc f c  Department of Electronic Engineering, NTUT80/140
81. 81. Oscillator Design (I) • Feedback : Barkhausen’s Criteria     ( ) ( ) 1 ( ) ( ) o f i V G s G s V G s H s  ( ) ( ) 1G s H s (Phase is 0 deg. or multiple of 360 deg.) Department of Electronic Engineering, NTUT81/140
82. 82. Oscillator Design (II)   ' 11 1G S   ' 22 1L S If the two-port network is oscillating at one port, it must be simultaneously oscillating at the other port. • Two Port Reflection Sine the resonator is passive, thus 1G  Department of Electronic Engineering, NTUT82/140
83. 83. Oscillator Design (III) 0)()(   DRR 0)()(   DXX • One-port Negative Resistance Department of Electronic Engineering, NTUT83/140
84. 84. Common Oscillator Configurations bi ci C E B 1C 2C 3L bi ci C E B 1L 2L 3C bi ci C E B 1C 2C 3L bi ci C E B 1C 2C 3L Colpitts Hartley Clapp Siler Department of Electronic Engineering, NTUT84/140
85. 85. Effects of Internal Noise Source • The nonlinearities in the circuit cause K1 or K2 to have a value such that the loop gain is unity, a condition for stable oscillation. • The other condition is that there be 360o phase shift around the loop. This occurs at the resonant frequency of the tank circuit. 2K RC L1 2i K v  1v nv 2v • If no feedback, the noise will appear at the output, amplified by K2. Department of Electronic Engineering, NTUT85/140
86. 86. Small Noise Introduced • But what effect does the feedback have? (1) Far from spectral center: the output contains amplified circuit noise (2) Close to spectral center: the feedback has an important effect            1 1 1 i T v Z i j C R L Phase shift of this factor is               1 1 tanT R C L 2K RC L1 2i K v  1v nv 2v Department of Electronic Engineering, NTUT86/140
87. 87. Tank Phase Shift 0 0 2Td Q d       Q is the loaded quality factor of the frequency-determining circuit. • For modulation rates small compared to one-half of the resonant bandwidth of ZT, a change in frequency causes a phase change in the transfer function, where the two changes are 2 osc Q      0 1 0 0 1 tan 0T R C L                   0   T 0 TH 1   Department of Electronic Engineering, NTUT87/140
88. 88. Phase Perturbations • The loop responds to a phase perturbation of by producing an equal and opposite phase change to maintain the required zero phase shift around the loop in the presence of modulation due to noise. This is done by shift the frequency. • A phase modulation with peak deviation due to noise vn necessitates frequency modulation of the oscillator output with peak deviation by     2 osc n n Q n n 0 T n n n Department of Electronic Engineering, NTUT88/140
89. 89. Closed-Loop Noise          2 2 oscn n m mQ where is the noise modulation frequency.  2 osc Q  1 m  n  n  2 • The phase noise would ordinarily appear at the output due to circuit noise is accentuated by a factor . 2osc mf Qf m 2 osc m f f Q  log mf Open loop Closed loop logS  2 rad Hz Department of Electronic Engineering, NTUT89/140
90. 90. Oscillator Phase Noise f 0f mff 0 1 Hz R P V avs avsRMS  R FkT VnRMS 11 Hz R FkT VnRMS 2 • The input phase noise in a 1-Hz bandwidth at any frequency from the carrier produces a phase deviation. 0 mf f sP nP  Department of Electronic Engineering, NTUT90/140 Noise
91. 91. Noise Caused Phase Deviation   1nRMS peak avsRMS avs V FkT V P  1 1 2 RMS avs FkT P  RMS total avs FkT P Noise  2 1 2 RMS avs FkT P (total phase deviation) 12 nRMSV m 2 avsRMSV 0  peak Department of Electronic Engineering, NTUT91/140
92. 92. Lesson’s Model (I) avs RMSm P FkTB fS  2 )(  1)(BdBm/Hz174 kTB S cf mf avsP FkTB 1)(B1)(        m c avs m f f P FkTB fS • The spectral density of phase noise : (theoretical noise floor of the amplifier) • Flicker Noise The purity of signal is degraded by the flicker noise at the frequencies close to the carrier. noise floor flicker noise Department of Electronic Engineering, NTUT92/140
93. 93. Lesson’s Model (II) ) 2 (1 1 )( 0   loadm m Qj L    in Equivalent lowpass for resonator out + )( min f )( 2 0 min mL f Qj          • The oscillator may be modeled as an amplifier with feedback 0 1 ( ) 2 1 L m L m H Q j            0 2 2L B Q   0 ( ) 1 ( ) 2 out m in m L m f f j Q               2 0 2 1 ( ) 1 ( ) 2 out m in m m L f S f S f f Q               ( ) 1 c in m avs m fFkTB S f P f          ( )L mH Department of Electronic Engineering, NTUT93/140
94. 94. Lesson’s Model (III) 2 2 3 2 2 1 1 L( ) 1 2 4 2 o c o c m avs m L m L m f f f fFkTB f P f Q f Q f              Up-convert 1/f noise Thermal FM noise Flicker noise Thermal noise floor • Lesson’s Oscillator Model: slope f cf f 1 Thermal Noise Floor 1/f noise at carrier 0f C              2 0 2 1 1 L( ) 1 ( ) 2 2 m in m m L f f S f f Q          ( ) 1 c in m avs m fFkTB S f P f Open-loop amp.Closed-loop with resonator Department of Electronic Engineering, NTUT94/140
95. 95. Lesson’s Model (IV) 1 mf 1 mf 0 mf 3 mf 1 mf 2 mf 3 mf 0 mf cf cf cf cf Q fo 2 Q fo 2 avsP FkTB avsP FkTB 2 avsP FkTB High Q Oscillator Phase perturbation Low Q Oscillator Phase perturbation Resulting phase noise Resulting phase noise Department of Electronic Engineering, NTUT95/140
96. 96. Noise Analysis
97. 97. PLL Phase Noise Model Frequency Divider ,ref n out 1 N PFD   LPF ,pfd nV ,op nV  ,vco n  ,div n VCO Xtal Department of Electronic Engineering, NTUT97/140
98. 98. Noise Transfer Functions (I)         , , , , , ,out n pfd n op n ref n div n e vco n d T s V V T s H s K                1 G s T s G s H s         1 1 eH s G s H s             for for1 c c NG s T s G sG s H s                   for1 for1 1 c e c N G sH s G s H s             Department of Electronic Engineering, NTUT98/140
99. 99. Noise Transfer Functions (II) c log m      1 G s G s H s N  G s Transfer function multiplying all sources except VCO c log m     1 1 G s H s 1     1 G s H s Transfer function for VCO c log m 20logN  G s  dB 0 Department of Electronic Engineering, NTUT99/140
100. 100. Typical VCO and PLL Noise Performance Department of Electronic Engineering, NTUT100/140
101. 101. PLL Design with Sheets http://www.peregrine-semi.com Department of Electronic Engineering, NTUT101/140
102. 102. Phase-Locked Loop Architectures • Integer-N PLL • Fractional-N PLL • Offset PLL • DDS Offset PLL • Dual Loop PLL • Multi-Loop PLL Department of Electronic Engineering, NTUT102/140
103. 103. Offset PLL out ref offsetf N f f   • Lower division ratio N to reduce inband phase-noise gain ? PFD LPF Frequency Divider reff outf /N offsetf • Extend bandwidth with different offsetf • Avoid LO pulling Department of Electronic Engineering, NTUT103/140
104. 104. Dual-Loop PLL (I) PFD LPF Frequency Divider reff outf /N offsetf PFD LPF outf /M 2nd loop Department of Electronic Engineering, NTUT104/140
105. 105. Dual-loop PLL (II) PFD LPF Frequency Divider 1reff outf/N 1f PFD LPF 2f /M 2nd loop 2reff Department of Electronic Engineering, NTUT105/140
106. 106. Multi-Loop PLL 3rd loop 2nd loop foffset1 PFD LPF /N foutVCOfref PFD LPF /M VCO foffset2 PFD LPF /P VCO foffset3 Department of Electronic Engineering, NTUT106/140
107. 107. DDS Offset PLL PFD LPF Frequency Divider reff outf /N offsetf DDS Department of Electronic Engineering, NTUT107/140
108. 108. Fractional-N Frequency Synthesis • Lower division ratio N to reduce inband phase-noise gain • Effectively produce a fractional division value • Generally employee a delta-sigma modulator for division ratio dithering PFD LPF Dual-modulus Frequency Divider reff outf /N, (N+1) FCW Department of Electronic Engineering, NTUT108/140
109. 109. DDS-Driven Fractional-N Synthesizer • DDS acts a reference source or phase/frequency modulator • A variable reference frequency source can drive a fractional frequency output. PFD LPF Frequency Divider reff outf /N DDS FCW Hybrid DDS/PLL Department of Electronic Engineering, NTUT109/140
110. 110. DDS-Feedback Fractional-N Synthesizer • DDS acts a frequency divider • DDS output frequency Hybrid DDS/PLL PFD LPF Frequency Divider reff outf DDS FCW 2 out ref offsetn M f f f   Department of Electronic Engineering, NTUT110/140
111. 111. Comparison of Frequency Synthesizers DDS Single-Loop PLL Multi-Loop PLL DDS/DAS DDS Offset PLL DDS Driven PLL BW (output) Narrow < 100MHz Broad > 1GHz Broad > 1GHz Broad > DDS Broad (carefully design) Broad Resolution Extremely Fine < 0.02 Hz Very Course > 250kHz (typical) Medium > 1kHz (typical) Extremely Fine < 0.01 Hz Extremely Fine < 0.01 Hz Extremely Fine < 1Hz Switching Time Very Fast < 100 ns Fast < 100us (typical) Very Slow > 1ms (typical) Very Fast < 1us (limited by RF switch) Fast < 100us (typical) Trade-off vs close-in spurious tones Spurious Noise < 75dBc (limited by DAC) Very Good Good (carefully design) Minimum Close-in Spurious Minimum Close-in Spurious Excellent over Broad Bandwidth Phase Noise Better than clock reference Very Good Very Good Very Good Very Good Good Circuitry Simple Simple Very Complex Moderate Moderate Moderate Department of Electronic Engineering, NTUT111/140
112. 112. PLL Simulation • ADS Circuit Envelope Simulation Basics • Integer-N Frequency Synthesizer Simulation • Fractional-N Frequency Synthesizer Simulation • Closed-In Phase Noise Characteristics Department of Electronic Engineering, NTUT112/140
113. 113. Circuit Envelope Simulation Technique • Time samples the modulation envelope (not carrier) • Compute the spectrum at each time sample • Output a time-varying spectrum • Use equations on the data • Faster than HB or SPICE in many case • Integrates with System Simulation & HP Ptolemy Department of Electronic Engineering, NTUT113/140
114. 114. What Test Can it Perform? • Test circuits with realistic signals Simulation can include: • Adjacent Channel Power Ratio • Noise Power Ratio • Error Vector Magnitude • Power Added Efficiency • Bit Error Rate Also, it can be used for PLL simulation: • Locking time • Spurious signal • Modulation in the loop • Phase noise Features of Circuit Envelope Simulation Department of Electronic Engineering, NTUT114/140
115. 115. • Time sample the envelope and then perform Harmonic Balance on the samples. V(t) can be complex – am, fm or pm Circuit Envelope Sampling Department of Electronic Engineering, NTUT115/140
116. 116. Spectrum Computation Department of Electronic Engineering, NTUT116/140
117. 117. Envelope Env1 Step=1 nsec Stop=100 nsec Order[1]=3 Freq[1]=1.0 GHz ENVELOPETime step – Determines bandwidth of Circuit Envelope simulation – Small enough to capture highest modulation frequency Stop time – Determines resolution bandwidth of output spectrum – Large enough to resolve spectral components of interest Frequency Span and Resolution Bandwidth Department of Electronic Engineering, NTUT117/140
118. 118. Vin Vout Envelope Env1 Step=1 nsec Stop=50 nsec Order[1]=1 Freq[1]=900 MHz ENVELOPE R R1 R=50 Ohm PtRF_Pulse PORT1 Period=100 nsec Width=30 nsec Fall=10 nsec Rise=5 nsec Delay=0 nsec OffRatio=0 Freq=900 MHz P=dbmtow(0) Z=50 Ohm Num=1 Amplifier AMP1 S12=0 S22=dbpolar(-50,0) S11=dbpolar(-50,0) S21=dbpolar(10,0) Circuit Envelope Simulation Example (I) Department of Electronic Engineering, NTUT118/140
119. 119. m2 time=5.000nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 m2 time=5.000nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 10 20 30 400 50 -0.5 0.0 0.5 -1.0 1.0 time, nsec real(Vin[1]) real(Vout[1]) m2 m1 ts(Vout),V m2 time=5.000nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 m2 time=5.000nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 10 20 30 400 50 -0.5 0.0 0.5 -1.0 1.0 time, nsec real(Vin[1]) real(Vout[1]) m2 m1 ts(Vout),V m2 time=10.00nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 m2 time=10.00nsec real(Vout[1])=1.000 m1 time=0.0000 sec real(Vout[1])=0.000 10 20 30 400 50 -0.5 0.0 0.5 -1.0 1.0 time, nsec real(Vin[1]) real(Vout[1]) m2 m1 ts(Vout),V m2 time=0.0000 sec real(Vout[1])=0.000 m1 time=0.0000 sec real(Vout[1])=0.000 m2 time=0.0000 sec real(Vout[1])=0.000 m1 time=0.0000 sec real(Vout[1])=0.000 10 20 30 40 500 60 -0.5 0.0 0.5 -1.0 1.0 time, nsec real(Vin[1]) real(Vout[1]) m2m1 ts(Vout),V Circuit Envelope Simulation Example (II) Department of Electronic Engineering, NTUT119/140 Tstep = 1 ns Tstep = 5 ns Tstep = 10 ns Tstep = 20 ns
120. 120. Integer-N Frequency Synthesizer
121. 121.     0out ch reff f k f M f    0out ch reff f k f M f For channel 1 (k=0)   0out L reff f M f    , 0,1,2, ,LM M k k N ch reff fch reff f Architecture of Integer-N Frequency Synthesizer 1 MHzreff  0 2.4 GHzf  2400N  Department of Electronic Engineering, NTUT121/140
122. 122. vtune VCOfreq VCOout Envelope Env1 Other= Step=Tstep Stop=4000*Tstep SweepOffset=0 StatusLevel=2 Order[1]=1 Freq[1]=fvco ENVELOPE V_1Tone SRC3 Freq=1 MHz V=polar(1,-90) V VAR VAR1 Tstep=1/(5*fref) DeltaN=(fvco+Deltaf)/fref -N0 Deltaf=0 MHz N0=fvco/fref fref=1 MHz fvco=2.4 GHz Eqn Var VtStep SRC4 Rise=1/fref Delay=0 nsec Vhigh=DeltaN V Vlow=0 Vt MeasEqn meas2 VCOfreqGHz=real(VCOfreq[0]) VCOphase=phase(VCOout[1]) fund=VCOout[1] Vtune=real(vtune[0]) Eqn Meas VCO_DivideByN VCO1 Delay=0 Power=dbmtow(10) Rout=50 Ohm N=N0 F0=fvco VCO_Freq=50 MHz * _v1 f r eq VCO . vcon - N. VCO t une dN C C3 C=100 pF R R3 R=50 Ohm R R4 R=50 Ohm ResetSwitch SWITCH1 t>0 t=0 C C2 C=16.4 nF R R1 R=3.3 kOhmC C1 C=1 nF R R2 R=15 kOhmPhaseFreqDetCP PFD1 Ilow=1 mA Ihigh=1 mA FREQ/CP I low I high PHASE/ VCO r ef Schematic of Integer-N Frequency Synthesizer PFD LPF VCO & Divider Output load Modulus Divided signal Department of Electronic Engineering, NTUT122/140
123. 123. -2 -1 0 1 2-3 3 -100 -50 0 -150 50 freq, MHz spectrum Reference Spurs (I) Reference spurs Department of Electronic Engineering, NTUT123/140
124. 124. Reference Spurs (II) Department of Electronic Engineering, NTUT124/140 A B UP DN A B AQ BQ Gate Delay (comparison transition)
125. 125. 100 200 300 400 500 600 7000 800 2.3999995 2.4000000 2.4000005 2.3999990 2.4000010 time, usec VCOfreqGHz 0 100 -0.000015 -0.000010 -0.000005 0.000000 0.000005 0.000010 -0.000020 0.000015 time, usec Vtune Improper LPF Design and Discrete Effect Department of Electronic Engineering, NTUT125/140
126. 126. m1 time=570.0000000usec VCOfreqGHz=2.401000000 m1 time=570.0000000usec VCOfreqGHz=2.401000000 100 200 300 400 5000 600 2.40 2.41 2.42 2.43 2.39 2.44 time, usec VCOfreqGHz m1 100 200 300 400 5000 600 0.0 0.2 0.4 0.6 -0.2 0.8 time, usec Vtune Eqn spectrum=dBm(fs(fund)) m2 freq=1000.kHz spectrum=10.00 m2 freq=1000.kHz spectrum=10.00 -2 -1 0 1 2-3 3 -150 -100 -50 0 -200 50 freq, MHz spectrum m2 VCO output spectrum at steady-state, jump from fcenter at 2.4GHz to 2.401GHz   1 MHzf PLL Transient Response (I) Department of Electronic Engineering, NTUT126/140
127. 127. m1 time=539.4000000usec VCOfreqGHz=2.410000000 m1 time=539.4000000usec VCOfreqGHz=2.410000000 100 200 300 400 5000 600 2.41 2.42 2.43 2.40 2.44 time, usec VCOfreqGHz m1 100 200 300 400 5000 600 0.2 0.4 0.6 0.0 0.8 time, usec Vtune m1 time=590.4000000usec VCOfreqGHz=2.480000000 m1 time=590.4000000usec VCOfreqGHz=2.480000000 100 200 300 400 5000 600 2.42 2.44 2.46 2.48 2.40 2.50 time, usec VCOfreqGHz m1 100 200 300 400 5000 600 0.5 1.0 1.5 0.0 2.0 time, usec Vtune   10 MHzf   80 MHzf PLL Transient Response (II) Department of Electronic Engineering, NTUT127/140
128. 128. Fractional-N Frequency Synthesizer
129. 129. ( 1) ( )A N M A N A N M M        ( ) ( )out ref ref A f N f N f M       Architecture of Fractional-N Frequency Synthesizer Department of Electronic Engineering, NTUT129/140
130. 130. deltaN vtune VCOfreq VCOout VAR VAR1 Tstep=1/(5*fref) Num=Denom*fraction Denom=20 fraction=DeltaN-intDeltaN intDeltaN=int(DeltaN) DeltaN=(fvco+Deltaf)/fref -N0 Deltaf=0.75 MHz N0=fvco/fref fref=1 MHz fvco=2.4 GHz Eqn Var MeasEqn meas2 VCOfreqGHz=real(VCOfreq[0]) VCOphase=phase(VCOout[1]) fund=VCOout[1] Vtune=real(vtune[0]) Eqn Meas Envelope Env1 Other= Step=Tstep Stop=4000*Tstep SweepOffset=0*Tstep StatusLevel=2 Order[1]=1 Freq[1]=fvco ENVELOPE C C3 C=100 pF R R2 R=15 kOhm R R1 R=3.3 kOhm C C2 C=16.4 nF V_1Tone SRC3 Freq=1 MHz V=polar(1,-90) V VtPulse SRC5 Period=Denom/fref Width=Num/fref Edge=linear Delay=(Denom-Num)/fref Vhigh=1 V Vlow=0 V t PhaseFreqDetCP PFD1 Ilow=1 mA Ihigh=1 mA FREQ/CP I low I high PHASE/ VCO ref VCO_DivideByN VCO1 Delay=0 Power=dbmtow(10) Rout=50 Ohm N=N0 F0=fvco VCO_Freq=50 MHz * _v1 f r eq VCO . vcon - N. VCO t une dN C C1 C=1 nF R R3 R=50 Ohm R R4 R=50 Ohm ResetSwitch SWITCH1 t>0 t=0 Schematic of Fractional-N Frequency Synthesizer Department of Electronic Engineering, NTUT130/140
131. 131. Denom (M) Num (A) VtPulse SRC5 Period=Denom/fref Width=Num/fref Delay=(Denom-Num)/fref Vhigh=1 V Vlow=0 V t VCO_DivideByN VCO1 freq VCO . vcon - N. VCO tune dN The Simulation Method Department of Electronic Engineering, NTUT131/140
132. 132. m1 time=227.000usec VCOfreqGHz=2.40005 100 200 300 400 500 600 7000 800 2.40 2.41 2.42 2.39 2.43 time, usec VCOfreqGHz m1  0.5 MHz 0.5 MHzreff f   PLL Transient Response Department of Electronic Engineering, NTUT132/140
133. 133. m2 freq=100.0kHz spectrum=-7.185 m1 freq=50.00kHz spectrum=9.827 m3 freq=150.0kHz spectrum=-28.277 m2 freq=100.0kHz spectrum=-7.185 m1 freq=50.00kHz spectrum=9.827 m3 freq=150.0kHz spectrum=-28.277 -2 -1 0 1 2-3 3 -80 -60 -40 -20 0 -100 20 f req, MHz spectrum m2 m1 m3 100 200 300 400 500 600 7000 800 2.40004 2.40005 2.40006 2.40003 2.40007 time, usec VCOfreqGHz m2 freq=800.0 spectrum= m1 freq=750.0 spectrum= m3 freq=850.0 spectrum= -2 -1 0 1 2-3 3 -60 -40 -20 0 -80 20 freq, MHz spectrum m2m1 m3 100 200 300 400 500 600 7000 800 2.40070 2.40075 2.40080 2.40065 2.40085 time, usec VCOfreqGHz Fractional Spurs Department of Electronic Engineering, NTUT133/140
134. 134. Closed-In Phase Noise Characteristics
135. 135. m1 freq=10.00kHz PN_Loop_Div_only=-87.846 m2 freq=100.0kHz PN_Loop_Div_only=-123.089 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -260 -40 freq, Hz PN_Loop_Div_only m1 m2 m1 freq=10.00kHz PN_Loop_Div_only=-88.255 m2 freq=100.0kHz PN_Loop_Div_only=-92.859 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -260 -40 freq, Hz PN_Loop_Div_only m1 m2 m1 freq=10.00kHz PN_Loop_Div_only=-112.609 m2 freq=100.0kHz PN_Loop_Div_only=-155.546 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -260 -40 freq, Hz PN_Loop_Div_only m1 m2 (1) (2) (3) (1) Loop BW = 1 kHz (2) Loop BW =10 kHz (3) Loop BW =100 kHz Phase Noise with Loop Divider Only Department of Electronic Engineering, NTUT135/140
136. 136. (1) (2) (3) (1) Loop BW = 1 kHz (2) Loop BW =10 kHz (3) Loop BW =100 kHz m1 freq=10.00kHz PN_PFD_only=-79.177 m2 freq=100.0kHz PN_PFD_only=-78.781 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -220 -200 -180 -160 -140 -120 -100 -80 -240 -60 freq, Hz PN_PFD_only m1 m2 m1 freq=10.00kHz PN_PFD_only=-103.531 m2 freq=100.0kHz PN_PFD_only=-141.468 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -220 -200 -180 -160 -140 -120 -100 -80 -240 -60 freq, Hz PN_PFD_only m1 m2 m1 freq=10.00kHz PN_PFD_only=-78.768 m2 freq=100.0kHz PN_PFD_only=-109.011 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -220 -200 -180 -160 -140 -120 -100 -80 -240 -60 freq, Hz PN_PFD_only m1 m2 Phase Noise with PFD Only Department of Electronic Engineering, NTUT136/140
137. 137. (1) (2) (3) m1 freq=10.00kHz PN_Ref_only=-88.246 m2 freq=100.0kHz PN_Ref_only=-92.857 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -260 -20 freq, Hz PN_Ref_only m1 m2 m1 freq=10.00kHz PN_Ref_only=-112.600 m2 freq=100.0kHz PN_Ref_only=-155.544 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -260 -20 freq, Hz PN_Ref_only m1 m2 m1 freq=10.00kHz PN_Ref_only=-87.837 m2 freq=100.0kHz PN_Ref_only=-123.087 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -260 -20 freq, Hz PN_Ref_only m1 m2 (1) Loop BW = 1 kHz (2) Loop BW =10 kHz (3) Loop BW =100 kHz Phase Noise with Reference Osc. Only Department of Electronic Engineering, NTUT137/140
138. 138. (1) (2) (3) m1 freq=10.00kHz PN_VCO_only=-126.536 m2 freq=100.0kHz PN_VCO_only=-112.256 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -195 -190 -185 -180 -175 -170 -165 -160 -155 -150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90 -85 -80 -75 -200 -70 freq, Hz PN_VCO_only m1 m2 m1 freq=10.00kHz PN_VCO_only=-96.380 m2 freq=100.0kHz PN_VCO_only=-112.580 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -195 -190 -185 -180 -175 -170 -165 -160 -155 -150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90 -85 -80 -75 -200 -70 freq, Hz PN_VCO_only m1 m2 m1 freq=10.00kHz PN_VCO_only=-96.443 m2 freq=100.0kHz PN_VCO_only=-112.315 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -195 -190 -185 -180 -175 -170 -165 -160 -155 -150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90 -85 -80 -75 -200 -70 freq, Hz PN_VCO_only m1 m2 (1) Loop BW = 1 kHz (2) Loop BW =10 kHz (3) Loop BW =100 kHz Phase Noise with VCO Only Department of Electronic Engineering, NTUT138/140
139. 139. (1) (2) (3) m1 freq=1.000kHz PNTotal=-75.603 m2 freq=10.00kHz PNTotal=-78.205 m3 freq=1.000kHz PN_VCO_only=-146.498 m4 freq=10.00kHz PN_VCO_only=-126.536 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -140 -120 -100 -80 -60 -40 -20 0 -160 20 f req, Hz PNTotal m1 m2 PN_VCO_only m3 m4PN_VCO_FreeRun m1 freq=1.000kHz PNTotal=-70.960 m2 freq=10.00kHz PNTotal=-93.347 m3 freq=1.000kHz PN_VCO_only=-76.978 m4 freq=10.00kHz PN_VCO_only=-96.380 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -140 -120 -100 -80 -60 -40 -20 0 -160 20 f req, Hz PNTotal m1 m2 PN_VCO_only m3 m4 PN_VCO_FreeRun m1 freq=1.000kHz PNTotal=-75.282 m2 freq=10.00kHz PNTotal=-76.852 m3 freq=1.000kHz PN_VCO_only=-106.753 m4 freq=10.00kHz PN_VCO_only=-96.443 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -140 -120 -100 -80 -60 -40 -20 0 -160 20 f req, Hz PNTotal m1 m2 PN_VCO_only m3 m4 PN_VCO_FreeRun (1) Loop BW = 1 kHz (2) Loop BW =10 kHz (3) Loop BW =100 kHz VCO in Loop vs. VCO Free-Running Department of Electronic Engineering, NTUT139/140
140. 140. (1) N = 2400 (2) N= 1400 m1 freq=1.000kHz PNTotal=-75.282 m2 freq=10.00kHz PNTotal=-76.852 m3 freq=1.000kHz PN_VCO_only=-106.753 m4 freq=10.00kHz PN_VCO_only=-96.443 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -140 -120 -100 -80 -60 -40 -20 0 -160 20 f req, Hz PNTotal m1 m2 PN_VCO_only m3 m4 PN_VCO_FreeRun m1 freq=1.000kHz PNTotal=-83.041 m2 freq=10.00kHz PNTotal=-83.673 m3 freq=1.000kHz PN_VCO_only=-114.513 m4 freq=10.00kHz PN_VCO_only=-103.265 10.00 100.0 1.000k 10.00k 100.0k 1.000M1.000 10.00M -140 -120 -100 -80 -60 -40 -20 0 -160 20 f req, Hz PNTotal m1 m2 PN_VCO_only m3 m4 PN_VCO_FreeRun Phase Noise with Various Modulus N Department of Electronic Engineering, NTUT140/140